Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update

Phenomenological Estimate of Isospin Breaking in Hadronic Vacuum Polarization

Puzzles in the determination of the hadronic-vacuum-polarization contribution currently impede a conclusive interpretation of the precision measurement of the anomalous magnetic moment of the muon at the Fermilab experiment. One such puzzle concerns tensions between evaluations in lattice QCD and using e^{+}e^{-}→hadrons cross-section data. In lattice QCD, the dominant isospin-symmetric part and isospin-breaking (IB) corrections are calculated separately, with very different systematic effects. Identifying these two pieces in a data-driven approach provides an opportunity to compare them individually and trace back the source of the discrepancy. Here, we estimate the IB component of the lattice-QCD calculations from phenomenology, based on a comprehensive study of exclusive contributions that can be enhanced via infrared singularities, threshold effects, or hadronic resonances, including, for the first time, in the e^{+}e^{-}→3π channel. We observe sizable cancellations among different channels, with a sum that even suggests a slightly larger result for the QED correction than obtained in lattice QCD. We conclude that the tensions between lattice QCD and e^{+}e^{-} data therefore cannot be explained by the IB contributions in the lattice-QCD calculations.

A dispersive analysis of η ' → π + π - γ and η ' → ℓ + ℓ - γ

We present a dispersive representation of the η ' transition form factor that allows one to account, in a consistent way, for the effects of ρ - ω mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on η ' → π + π - γ to constrain the isovector part of the form factor, individually and in combination with data for the pion vector form factor, which suggests a tension in the ρ - ω mixing parameter. As a first application, we use our results, in combination with the most recent input for the isoscalar part of the form factor, to predict the corresponding spectrum of η ' → ℓ + ℓ - γ , in particular we find the slope parameter b η ' = 1.455 ( 24 ) GeV - 2 . With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the η ' -pole contribution to the anomalous magnetic moment of the muon using experimental input from both η ' decay channels.

Kaon electromagnetic form factors in dispersion theory

The electromagnetic form factors of charged and neutral kaons are strongly constrained by their low-energy singularities, in the isovector part from two-pion intermediate states and in the isoscalar contribution in terms of ω and ϕ residues. The former can be predicted using the respective π π → K ¯ K partial-wave amplitude and the pion electromagnetic form factor, while the latter parameters need to be determined from electromagnetic reactions involving kaons. We present a global analysis of time- and spacelike data that implements all of these constraints. The results enable manifold applications: kaon charge radii, elastic contributions to the kaon electromagnetic self energies and corrections to Dashen's theorem, kaon boxes in hadronic light-by-light (HLbL) scattering, and the ϕ region in hadronic vacuum polarization (HVP). Our main results are: ⟨ r 2 ⟩ c = 0.359 ( 3 ) fm 2 , ⟨ r 2 ⟩ n = - 0.060 ( 4 ) fm 2 for the charged and neutral radii, ϵ = 0.63 ( 40 ) for the elastic contribution to the violation of Dashen's theorem, a μ K -box = - 0.48 ( 1 ) × 10 - 11 for the charged kaon box in HLbL scattering, and a μ HVP [ K + K - , ≤ 1.05 GeV ] = 184.5 ( 2.0 ) × 10 - 11 , a μ HVP [ K S K L , ≤ 1.05 GeV ] = 118.3 ( 1.5 ) × 10 - 11 for the HVP integrals around the ϕ resonance. The global fit to K ¯ K gives M ¯ ϕ = 1019.479 ( 5 ) MeV , Γ ¯ ϕ = 4.207 ( 8 ) MeV for the ϕ resonance parameters including vacuum-polarization effects.

Mixed Leptonic and Hadronic Corrections to the Anomalous Magnetic Moment of the Muon

Higher-order hadronic corrections to the anomalous magnetic moment of the muon have been evaluated including next-to-next-to-leading-order insertions of hadronic vacuum polarization and next-to-leading-order corrections to hadronic light-by-light scattering. This leaves a set of mixed leptonic and hadronic corrections in the form of double-bubble topologies as the only remaining hadronic effect at O(α^{4}). Here, we estimate these contributions by analyzing the respective cuts of the diagrams, suggesting that the impact is limited to ≲1×10^{-11} and thus negligible at the level of the final precision of the Fermilab g-2 experiment.

Data-driven approaches to the evaluation of hadronic contributions to the (g − 2)μ

In this talk I reviewed the data-driven theoretical calculation of the hadronic contributions to the anomalous magnetic moment of the muon in the Standard Model mainly as it has been presented in the White Paper, but also including the most recent developments. All this is presented in the light of the new measurement of (g − 2)μ recently released by the Fermilab experiment, which led to an increase of the discrepancy with the Standard Model from 3.7 to 4.2σ.

Recent progress in hadronic light-by-light scattering

In recent years, significant progress in the calculation of the HLbL contribution to the anomalous magnetic moment of the muon has been achieved both with data-driven methods and in lattice QCD. In these proceedings I will discuss current developments aimed at controlling HLbL scattering at the level of 10%, as required for the final precision of the Fermilab E989 experiment.

Short-distance constraints for HLbL in muon g-2

Model-independent short-distance constraints allow for a reduction of theoretical uncertainties associated to the analytic evaluation of Hadronic Light-by-Light contributions to the muon g-2. In this talk we focus on the region where the three loop virtualities are large. Even when the fourth photon leg is soft, we show how a precise Operator Product Expansion can be applied in that region. The leading contribution is found to be given by the quark loop, while the evaluation of both gluonic and power corrections show how the expansion is well behaved at relatively low energies, where significant contributions to the muon g-2 remain. Numerical values for them are also presented.

Short-distance constraints on the hadronic light-by-light

The muon anomalous magnetic moment continues to attract interest due to the potential tension between experimental measurement [1, 2] and the Standard Model prediction [3]. The hadronic light-by-light contribution to the magnetic moment is one of the two diagrammatic topologies currently saturating the theoretical uncertainty. With the aim of improving precision on the hadronic light-by-light in a data-driven approach founded on dispersion theory [4, 5], we derive various short-distance constraints of the underlying correlation function of four electromagnetic currents. Here, we present our previous progress in the purely short-distance regime and current efforts in the so-called Melnikov-Vainshtein limit.

Hadronic ligh-by-light contribution to the anomalous magnetic moment of the muon: The role of scalar resonances in a holographic model of QCD

We review the evaluation of scalar mesons contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment, using a holographic model of QCD.We evaluate the contributions of the lightest, sub-GeV scalars σ(500), a0(980) and f0(980) and their associated towers of excited states. Our results point at a negative contribution, overwhelmingly dominated by the σ(500) meson, that we estimate at aμHLbL,S = -9(2)·10-11, in very good agreement with recent determinations from dispersive analyses.

Holographic QCD and the muon anomalous magnetic moment

We review the recent progress made in using holographic QCD to study hadronic contributions to the anomalous magnetic moment of the muon, in particular the hadronic light-by-light scattering contribution, where the short-distance constraints associated with the axial anomaly are notoriously difficult to satisfy in hadronic models. This requires the summation of an infinite tower of axial vector mesons, which is naturally present in holographic QCD models, and indeed takes care of the longitudinal short-distance constraint due to Melnikov and Vainshtein. Numerically the results of simple hard-wall holographic QCD models point to larger contributions from axial vector mesons than assumed previously, while the predicted contributions from pseudo-Goldstone bosons agree nicely with data-driven approaches.

Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update

We reassess the impact of short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude on the anomalous magnetic moment of the muon, a μ = ( g - 2 ) μ / 2 , by comparing different solutions that have recently appeared in the literature. In particular, we analyze the relevance of the exact axial anomaly and its impact on a μ and conclude that it remains rather limited. We show that all recently proposed solutions agree well within uncertainties on the numerical estimate of the impact of short-distance constraints on a μ , despite differences in the concrete implementation. We also take into account the recently calculated perturbative corrections to the massless quark loop to update our estimate and outline the path towards future improvements.